1. Field of the Invention
The present invention relates to a digital electrophotographic imaging apparatus in which a latent electrostatic image is formed by exposing a photoreceptor by using an optical beam such as a laser beam and the image is visualized by a toner.
2. Description of the Background Art
Table 1 represents relation of resolution per inch (DPI: Dot Per Inch) of a laser beam printer, dot pitch Dp corresponding to the resolution and average beam diameters employed. It can be seen from the table that resolution of the optical system cannot follow the resolution of the printer, as the resolution increases.
FIG. 2 is a schematic diagram of a laser beam scanning optics, in which a light beam 45 emitted from a laser light source 44 passes through a collimator lens 46 and a cylindrical lens 47, reflected by a polygon mirror 41 and forms an image on a photoreceptor drum 2. As polygon mirror 41 rotates, the light beam scans the photoreceptor drum 2. FIG. 3 is an enlarged view of the image forming portion. The expansion of the image forming beam (beam diameter) Ds with no aberration is given by the following equation, where xcex represents the wavelength of the laser beam, f represents focal length of the lens and D represents pupil diameter of the laser beam.
xe2x80x83Ds=2xcex/(xcfx80xc2x7NA)=4xcexxc2x7f/(xcfx80xc2x7D)
The focal length f of the laser scanning optics must be as large as necessary for scanning an A3 object. Therefore, in order to make smaller the beam diameter Ds, it is necessary to shorten the wavelength xcex or to enlarge the pupil diameter D. In order to use a light source having shorter wavelength, the design of the optics must be changed and the photoreceptor material must be reviewed in accordance with the wavelength. When the pupil diameter D is enlarged, the optics becomes larger, and therefore, it is difficult to positively make smaller the beam diameter Ds in practice.
FIGS. 1A to 1C represent relations between the beam diameter Ds and the dot pitch Dp. When the beam diameter Ds and the dot pitch Dp are equal to each other, the ratio of the width W1 of 1 line with respect to the width W2 for 2 lines is 1:2. When the beam diameter Ds becomes larger than the dot pitch Dp, the relation of 1:2 is lost gradually.
Therefore, as can be seen from Table 1, in a current laser beam scanning apparatus, when the resolution is 600 DPI or higher, the ratio between the beam diameter Ds and the dot pitch Dp attains to 2 or higher. Therefore, it becomes difficult to ensure the ratio of the width W1 of 1 line with respect to the width W2 of 2 lines of 1:2.
The present invention was made in view of the foregoing and its object is to provide an electrophotographic imaging apparatus in which a toner image obtained by development can be fixed at a desired ratio (the ratio of the width of 1 line with respect to the width of 2 lines is 1:2) even when the beam diameter is larger than the dot pitch.
The above described object can be attained by an electrophotographic imaging apparatus employing a digital electrophotographic imaging process in which a latent electrostatistic image is written discretely by exposure modulation means on a charged photoreceptor and the image is visualized by development, characterized in that an unsaturated region of photo-induced discharge characteristic or gamma characteristics of development of the photoreceptor is used when an image of 1 dot or a 1-dot line, that is an image of which lines consist of single dots to be formed, and a saturated region of photo-induced discharge characteristics or gamma characteristics of development is used when an image of 2 dots or at least 2-dots line is to be formed.
Though FIGS. 1A to 1C schematically show the relation between the beam diameter Ds and the line width W, in an actual digital electrophotographic imaging process, exposure energy in accordance with image information is emitted from an exposure apparatus 4 to a photoreceptor 2 which has been uniformly charged by a charger 3, charges at the irradiated portion are lost and a latent image profile is formed, as shown in FIG. 4. Thereafter, charged toner 10 is fixed on the portion where the charges have been lost, by developing means 11, so that a development profile as a toner image is formed. More specifically, an image pattern including images of 1 line and 2 lines is converted through an exposure profile and a latent image profile to a development profile.
The exposure profile depends on power and size of an exposure beam as well as on exposure time. The process in which the exposure profile is determined will be described with reference to laser scanning as an example. Energy distribution I (x, y) per unit time when a Gaussian laser beam, which has laser power P and beam radius of wx, wy, is static is given by the equation (2).                               I          ⁡                      (                          x              ,              y                        )                          =                                            2              ⁢              P                                      π              ·              wx              ·              wy                                ⁢                      Exp            ⁡                          (                                                -                                                            2                      ⁢                                              x                        2                                                                                    wx                      2                                                                      -                                                      2                    ⁢                                          y                      2                                                                            wy                    2                                                              )                                                          (        2        )            
Exposure energy profile Ev (x, y) when pulse width is xcex94t and scanning rate is v is given by the equation (3).                               Ev          ⁡                      (                          x              ,              y                        )                          =                                            ∫              0                              Δ                ⁢                                  xe2x80x83                                ⁢                t                                      ⁢                                          I                ⁡                                  (                                                            x                      -                                              v                        ·                        t                                                              ,                    y                                    )                                            ⁢                              ⅆ                t                                              =                                                    2                ⁢                P                                            π                ·                wx                ·                wy                                      ⁢                          Exp              ⁡                              (                                  -                                                            2                      ⁢                                              y                        2                                                                                    wy                      2                                                                      )                                      ⁢                                          ∫                0                                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                            ⁢                                                Exp                  ⁡                                      (                                          -                                                                        2                          ⁢                                                                                    (                                                              x                                -                                                                  v                                  ·                                  t                                                                                            )                                                        2                                                                                                    wx                          2                                                                                      )                                                  ⁢                                  ⅆ                  t                                                                                        (        3        )            
In digital exposure, when we represent exposure coordinates as (xi, yj), xi and yj assume discrete values dependent on the resolution. For example, when it is 1200 DPI, the dot pitch Dp is about 20 xcexcm, and therefore, x1, x2, . . . will be x1, x2, . . . =0, 20, 40, 60, . . . Assume that a function G (xi, yj) representing the state of exposure of the coordinates (xi, yj) is defined by equation (4).                               G          ⁡                      (                                          x                i                            ,                              y                i                                      )                          =                  {                                                    1                                                              laser ON                                                                                    0                                                              laser OFF                                                                                        (        4        )            
Then, a total exposure profile En (x, y) is given by the following equation (5).                                           E            n                    ⁡                      (                          x              ,              y                        )                          =                              ∑            i                    ⁢                                    ∑              j                        ⁢                                          Ev                ⁡                                  (                                                            x                      -                                              x                        i                                                              ,                                          y                      -                                              y                        j                                                                              )                                            ·                              G                ⁡                                  (                                                            x                      i                                        ,                                          y                      j                                                        )                                                                                        (        5        )            
FIG. 6 represents the image profile transfer function of FIG. 5 plotted in detail as a graph. Specifically, it is a chart plotting the process in which an exposure profile corresponding to image information of 1 line and 2 lines having the pixel density of 1200 DPI is converted to a latent image profile in accordance with photo-induced discharge characteristics of photoreceptor 2, and further converted to a development profile in accordance with the gamma characteristics of development.
The exposure beam has a power of 0.2 mW and beam diameter of 60 xcexcm. Exposure time per dot is 17.76 nsec, and scanning rate is 1191.9 m/sec. Initial potential voltage after charging of photoreceptor 2 is xe2x88x92600V, and half-decay exposure energy is 0.1 xcexcJ/cm2. More specifically, the characteristic is such that when irradiated with optical energy density of 0.1 xcexcJ/cm2, photoreceptor potential falls to xe2x88x92300V, that is, xc2xd of the initial potential voltage after charging.
In this example, the peak values of exposure energy distribution of 1 line and 2 lines both attain to the saturation values of photo-induced discharge characteristics of the photoreceptor, and the latent image profile and the development profile are both truncated profiles. Therefore, it is impossible to attain the line width ratio W1 and W2 of 1 line and 2 lines, that is, W1:W2 to 1:2. Further, the line width of 1 line attains to 45 xcexcm when the adhesion amount is 0.4 mg/cm2 (amount of adhesion corresponding to one layer of toner having average grain diameter of 7 xcexcm), which is larger than the target value (about 25 xcexcm) of the width of 1 line with 1200 DPI.
FIG. 7 shows an example in which a latent image is formed using an unsaturated region of the photo-induced discharge characteristics of the photoreceptor. The power of the exposure beam was set to 0.12 mW, and half-decay exposure energy Eh of the photoreceptor was set to 0.19 xcexcJ/cm2. The charge potential of the photoreceptor is xe2x88x92600V and the residual potential voltage after exposure VL is xe2x88x9260V. Surface potential V1 when the photoreceptor receives the exposure energy Et can be modeled by the following equation (6).                               Ev          ⁡                      (                          x              ,              y                        )                          =                                            ∫              0                              Δ                ⁢                                  xe2x80x83                                ⁢                t                                      ⁢                                          I                ⁡                                  (                                                            x                      -                                              v                        ·                        t                                                              ,                    y                                    )                                            ⁢                              ⅆ                t                                              =                                                    2                ⁢                P                                            π                ·                wx                ·                wy                                      ⁢                          Exp              ⁡                              (                                  -                                                            2                      ⁢                                              y                        2                                                                                    wy                      2                                                                      )                                      ⁢                                          ∫                0                                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                            ⁢                                                Exp                  ⁡                                      (                                          -                                                                        2                          ⁢                                                                                    (                                                              x                                -                                                                  v                                  ·                                  t                                                                                            )                                                        2                                                                                                    wx                          2                                                                                      )                                                  ⁢                                  ⅆ                  t                                                                                        (        6        )            
FIG. 8 is a graph representing the actual measurement of the photo-induced discharge characteristic of the photoreceptor and model given by the equation (6). The saturated region of the photoreceptor is the region in which Vi=VL. When we represent the exposure energy Et by Ek, we can obtain equation (1).
Ek=2(|V0xe2x88x92VL)xc2xd÷{2(|V0xe2x88x92VL|)xc2xdxe2x88x92{square root over (2)}(|V0xe2x88x922VL|)xc2xd}xc2x7Ehxe2x80x83xe2x80x83(1)
The threshold energy for saturation Ek of the photoreceptor used in FIGS. 7 and 8 calculated accordingly is 0.75 xcexcJ/cm2. Therefore, the exposure energies of 1 line and 2 lines shown in FIG. 7 are both in the unsaturated region of the photoreceptor.
Next, the gamma characteristics of development will be considered. When we represent the potential at the start of development by Vth, saturation potential for development by Vm, saturation development amount by Wm, potential of the image portion of the photoreceptor by Vi and development bias by VB, the amount of development per unit area M/A can be modeled by the equation (7).                                                                                                               when                                    ⁢                                      xe2x80x83                                    ⁢                                      V                    i                                                   less than                                   V                  th                                                                                                                          M                  /                  A                                =                0                                                                                                                              when                                    ⁢                                      xe2x80x83                                    ⁢                                      V                    th                                                  ≦                                  V                  i                                ≦                                  V                  m                                                                                                                          M                  /                  A                                =                                                      -                                                                                            W                          m                                                ·                                                  V                          th                                                                                                                      W                          m                                                -                                                  V                          th                                                                                                      +                                                                                    W                        m                                                                                              V                          m                                                -                                                  V                          th                                                                                      ·                                          (                                                                        V                          i                                                -                                                  V                          B                                                                    )                                                                                                                                                                                    when                                    ⁢                                      xe2x80x83                                    ⁢                                      V                    i                                                   greater than                                   V                  m                                                                                                                          M                  /                  A                                =                                  W                  m                                                                    }                            (        7        )            
FIG. 9 shows a model curve and experimental data. In the example shown in FIG. 7, the gamma characteristics of development and development bias are set such that the amount of development is in an unsaturated region for a portion of 1 line and in a saturated region for a portion of 2 lines.
More specifically, the development characteristics of Vth=xe2x88x92100V, Vm=200V, Wm=0.6 mg/cm2 were employed, and the development bias was set to VB=xe2x88x92400V.
As a result, the development profile ratio of 1 line and 2 lines could be set to 1:2. In this manner, by using the unsaturated region of the photoreceptor, it becomes possible to set the ratio of development widths of 1 line and 2 lines to 1:2.
Therefore, in the present invention, means for attaining the above described object is structured in the following manner.
(1) In a digital electrophotographic imaging apparatus writing a latent electrostatic image to a charged photoreceptor using an exposure beam diameter Ds larger than a pixel pitch Dp and visualizing the image by development, an unsaturated region of photo-induced discharge characteristics of the photoreceptor is used for an image portion of an isolated 1 line, and a saturated region of photo-induced discharge characteristic of the photoreceptor or gamma characteristics of development is used for the image portion of n lines (nxe2x89xa72).
By this structure, even when the beam diameter is larger than the dot pitch, it is possible to fix a toner image obtained by development with a desired ratio (the ratio of development widths of 1 line and 2 lines being 1:2), and necessary image density is ensured.
(2) In a digital electrophotographic imaging apparatus writing a latent electrostatic image discretely to a charged photoreceptor by using an exposure beam diameter Ds larger than pixel pitch Dp and visualizing the image by development, the pixel pitch Dp and the exposure beam diameter Ds satisfy the relation of Dp less than Dsxe2x89xa6{square root over ( )}2Dp, a saturated region of photo-induced discharge characteristics of the photoreceptor or gamma characteristics of development is used for an image portion of isolated 1 dot, and a saturated region of the photo-induced discharge characteristics of the photoreceptor or gamma characteristics of development is used for the image portion for n lines (nxe2x89xa72).
By this structure, even when the beam diameter is larger than the dot pitch, it is possible to fix a toner image obtained by development with a desired ratio (the ratio of development widths of 1 line and 2 lines being 1:2), and necessary image density is ensured.
(3) The saturated region of photo-induced discharge characteristics of photoreceptor means a region where potential of the photoreceptor hardly lowers with respect to increment of exposure energy directed to the photoreceptor, exposure energy Ek as a threshold value is represented by equation (1) where V0 represents charge potential of the photoreceptor, VL represents residual potential voltage after exposure and Eh represents half-decay exposure energy:
xe2x80x83Ek=2(|V0xe2x88x92VL|)xc2xd÷{2(|V0xe2x88x92VL|)xc2xdxe2x88x92{square root over (2(|V0xe2x88x922VL|){fraction (1/2)})}}xc2x7Ehxe2x80x83xe2x80x83(1)
and the region where the exposure energy is not smaller than Ek is determined to be a saturated region and a region where the exposure energy is smaller than Ek is determined to be an unsaturated region.
By this structure, even when the beam diameter is larger than the dot pitch, it is possible to fix a toner image obtained by development with a desired ratio, and necessary image density is ensured.
(4) The following relation is set where Er represents an energy level when ratio between extension width of exposure energy distribution of the isolated 1 line and extension width of exposure energy distribution of 2 lines is 1:2, Eh represents exposure energy when initial potential of the photoreceptor is half-decayed, and Ek represents exposure energy as a threshold value thereof:
Ehxe2x89xa6Er less than Ek.
By this structure, when the unsaturated region of the photoreceptor is used, the ratio of the development profile can be obtained while substantially maintaining the ratio of the exposure energy profile determined by Er.
(5) The following relation is set where Er represents an energy level when ratio between extension width of exposure energy distribution of the isolated 1 line and extension width of exposure energy distribution of 2 lines is 1:2, Eh represents exposure energy when initial potential of the photoreceptor is half-decayed, and Ek represents exposure energy as a threshold value thereof:
Ehxe2x89xa6Er less than Ek,
and
saturated region of the gamma characteristics of development is used both for the isolated 1 line and 2 lines.
By this structure, a development profile which is stable and insensitive to the variation of development characteristics can be obtained.
The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.